In the question, the probability of getting the given number of success
from a specified number of trials is required.
The correct probability function to use is the <u>binomial probability function</u>.
Reasons:
The given parameters are;
The probability of success = 0.06
The number of trials = 15 trials
The probability of interest = The probability of two successes in 15 trials
Solution;
The required probability is given by the following binomial probability
distribution formula;
![P(x) = \dbinom{n}{x}\cdot p^x \cdot q^x = \mathbf{\dfrac{n!}{(n - x)! \cdot x!} \cdot p^x \cdot q^x}](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%5Cdbinom%7Bn%7D%7Bx%7D%5Ccdot%20p%5Ex%20%5Ccdot%20q%5Ex%20%3D%20%5Cmathbf%7B%5Cdfrac%7Bn%21%7D%7B%28n%20-%20x%29%21%20%5Ccdot%20x%21%7D%20%5Ccdot%20p%5Ex%20%5Ccdot%20q%5Ex%7D)
Where:
n = Number of trials
x = Number of required success
p = Probability of a success
q = Probability of one failure = 1 - p
For the question, we get;
![P(x) = \dfrac{15!}{(15 - 2)! \times 2!} \times 0.06^2 \times (1 - 0.06)^{15 - 2} \approx \mathbf{0.169}](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%20%5Cdfrac%7B15%21%7D%7B%2815%20-%202%29%21%20%5Ctimes%202%21%7D%20%5Ctimes%200.06%5E2%20%5Ctimes%20%281%20-%200.06%29%5E%7B15%20-%202%7D%20%5Capprox%20%20%5Cmathbf%7B0.169%7D)
Therefore, the correct option is, a <u>binomial probability function</u>
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Learn more here:
brainly.com/question/15902935
<em>The question options are;</em>
<em>Binomial probability function</em>
<em>Normal probability density function</em>
<em>Standard normal probability density function</em>
<em>Poisson probability function</em>